Near wake vortex dynamics of a hovering hawkmoth

Numerical investigation of vortex dynamics in near wake of a hovering hawkmoth and hovering aerodynamics is conducted to support the development of a biology-inspired dynamic flight simulator for flapping wingbased micro air vehicles. Realistic wing-body morphologies and kinematics are adopted in the numerical simulations. The computed results show 3D mechanisms of vortical flow structures in hawkmoth-like hovering. A horseshoe-shaped primary vortex is observed to wrap around each wing during the early down- and upstroke; the horseshoe-shaped vortex subsequently grows into a doughnut-shaped vortex ring with an intense jet-flow present in its core, forming a downwash. The doughnut-shaped vortex rings of the wing pair eventu- ally break up into two circular vortex rings as they propagate downstream in the wake. The aerodynamic yawing and rolling torques are canceled out due to the symmetric wing kinematics even though the aerodynamic pitching torque shows significant variation with time. On the other hand, the time- varying the aerodynamics pitching torque could make the body a longitudinal oscillation over one flapping cycle.     

Effects of wing deformation on aerodynamic performance of a revolving insect wing

Flexible wings of insects and bio-inspired micro air vehicles generally deform remarkably during flapping flight owing to aerodynamic and inertial forces,which is of highly nonlinear fluid-structure interaction（FSI）problems.To elucidate the novel mechanisms associated with flexible wing aerodynamics in the low Reynolds number regime,we have built up a FSI model of a hawkmoth wing undergoing revolving and made an investigation on the effects of flexible wing deformation on aerodynamic performance of the revolving wing model.To take into account the characteristics of flapping wing kinematics we designed a kinematic model for the revolving wing in two-fold：acceleration and steady rotation,which are based on hovering wing kinematics of hawkmoth,Manduca sexta.Our results show that both aerodynamic and inertial forces demonstrate a pronounced increase during acceleration phase,which results in a significant wing deformation.While the aerodynamic force turns to reduce after the wing acceleration terminates due to the burst and detachment of leading-edge vortices（LEVs）,the dynamic wing deformation seem to delay the burst of LEVs and hence to augment the aerodynamic force during and even after the acceleration.During the phase of steady rotation,the flexible wing model generates more ver-tical force at higher angles of attack（40°–60°）but less horizontal force than those of a rigid wing model.This is because the wing twist in spanwise owing to aerodynamic forces results in a reduction in the effective angle of attack at wing tip,which leads to enhancing the aerodynamics performance by increasing the vertical force while reducing the horizontal force.Moreover,our results point out the importance of the fluid-structure interaction in evaluating flexible wing aerodynamics：the wing deformation does play a significant role in enhancing the aerodynamic performances but works differently during acceleration and steady rotation,which is mainly induced by inertial force in acceleration but by aerodynamic forces     

Effects of unsteady deformation of flapping wing on its aerodynamic forces

Effects of unsteady deformation of a flapping model insect wing on its aerodynamic force production are studied by solving the Navier-Stokes equations on a dynamically deforming grid.Aerodynamic forces on the flapping wing are not much affected by considerable twist,but affected by camber deformation.The effect of combined camber and twist deformation is similar to that of camber deformation.With a deformation of 6% camber and 20°twist(typical values observed for wings of many insects),lift is increased bv 10%～20%and lift-to-drag ratio by around 10%compared with the case of a rigid flat-plate wing.As a result.the deformation can increase the maximum lift coefficient of an insect.and reduce its power requirement for flight.For example,for a hovering bumblebee with dynamically deforming wings(6?mber and 20°twist),aerodynamic power required is reduced by about 16%compared with the case of rigid wings.     

Wing kinematics measurement and aerodynamics of free-flight maneuvers in drone-flies

The time courses of wing and body kinematics of two free-flying drone-flies, as they performed saccades, were measured using 3D high-speed video, and the morpho- logical parameters of the wings and body of the insects were also measured. The measured wing kinematics was used in a Navier-Stokes solver to compute the aerodynamic forces and moments acting on the insects. The main results are as following. （1） The turn is mainly a 90° change of heading. It is made in about 10 wingbeats （about 55 ms）. It is of interest to note that the number of wingbeats taken to make the turn is approximately the same as and the turning time is only a little different from that of fruitflies measured recently by the same approach, even if the weight of the droneflies is more than 100 times larger than that of the fruitflies. The long axis of body is about 40° from the horizontal during the maneuver. （2） Although the body rotation is mainly about a vertical axis, a relatively large moment around the yaw axis （axis perpendicular to the long axis of body）, called as yaw moment, is mainly needed for the turn, because moment of inertial of the body about the yaw axis is much larger than that about the long axis. （3） The yaw moment is mainly pro- duced by changes in wing angles of attack： in a right turn, for example, the dronefly lets its right wing to have a rather large angle of attack in the downstroke （generally larger than 50°） and a small one in the upstroke to start the turn, and lets its left wing to do so to stop the turn, unlike the fruitflies who generate the yaw moment mainly by changes in the stroke plane and stroke amplitude.     

Aerodynamic interaction between forewing and hindwing of a hovering dragonfly

The phase change between the forewing and hindwing is a distinct feature that sets dragonfly apart from other insects.In this paper,we investigated the aerodynamic effects of varying forewing-hindwing phase di ff erence with a60 inclined stroke plane during hovering flight.Force measurements on a pair of mechanical wing models showed that in-phase flight enhanced the forewing lift by 17%and the hindwing lift was reduced at most phase differences.The total lift of both wings was also reduced at most phase di ff erences and only increased at a phase range around in-phase.The results may explain the commonly observed behavior of the dragonfly where 0 is employed in acceleration.We further investigated the wing-wing interaction mechanism using the digital particle image velocimetry（PIV）system,and found that the forewing generated a downwash flow which is responsible for the lift reduction on the hindwing.On the other hand,an upwash flow resulted from the leading edge vortex of the hindwing helps to enhance lift on the forewing.The results suggest that the dragonflies alter the phase di ff erences to control timing of the occurrence of flow interactions to achieve certain aerodynamic effects.     

Aerodynamic mechanism of forces generated by twisting model-wing in bat flapping flight

The aerodynamic mechanism of the bat wing membrane Mong the lateral border of its body is studied. The twist-morphing that alters the angle of attack （AOA） along the span-wise direction is observed widely during bat flapping flight. An assumption is made that the linearly distributed AOA is along the span-wise direction. The plate with the aspect ratio of 3 is used to model a bat wing. A three-dimensional （3D） unsteady panel method is used to predict the aerodynamic forces generated by the flapping plate with leading edge separation. It is found that, relative to the rigid wing flapping, twisting motion can increase the averaged lift by as much as 25% and produce thrust instead of drag. Furthermore, the aerodynamic forces （lift/drag） generated by a twisting plate-wing are similar to those of a pitching rigid-wing, meaning that the twisting in bat flight has the same function as the supination/pronation motion in insect flight.     

Micro air vehicle-motivated computational biomechanics in bio-flights: aerodynamics, flight dynamics and maneuvering stability

Aiming at developing an effective tool to unveil key mechanisms in bio-flight as well as to provide guidelines for bio-inspired micro air vehicles（MAVs） design,we propose a comprehensive computational framework,which integrates aerodynamics,flight dynamics,vehicle stability and maneuverability.This framework consists of（1） a Navier-Stokes unsteady aerodynamic model;（2） a linear finite element model for structural dynamics;（3） a fluidstructure interaction（FSI） model for coupled flexible wing aerodynamics aeroelasticity;（4） a free-flying rigid body dynamic（RBD） model utilizing the Newtonian-Euler equations of 6DoF motion;and（5） flight simulator accounting for realistic wing-body morphology,flapping-wing and body kinematics,and a coupling model accounting for the nonlinear 6DoF flight dynamics and stability of insect flapping flight.Results are presented based on hovering aerodynamics with rigid and flexible wings of hawkmoth and fruitfly.The present approach can support systematic analyses of bio- and bio-inspired flight.     

Dynamic flight stability of hovering model insects: theory versus simulation using equations of motion coupled with Navier–Stokes equations

In the present paper, the longitudinal dynamic flight stability properties of two model insects are predicted by an approximate theory and computed by numerical sim- ulation. The theory is based on the averaged model （which assumes that the frequency of wingbeat is sufficiently higher than that of the body motion, so that the flapping wings＇ degrees of freedom relative to the body can be dropped and the wings can be replaced by wingbeat-cycle-average forces and moments）; the simulation solves the complete equations of motion coupled with the Navier-Stokes equations. Comparison between the theory and the simulation provides a test to the validity of the assumptions in the theory. One of the insects is a model dronefly which has relatively high wingbeat frequency （164 Hz） and the other is a model hawkmoth which has relatively low wingbeat frequency （26 Hz）. The results show that the averaged model is valid for the hawkmoth as well as for the dronefly. Since the wingbeat frequency of the hawkmoth is relatively low （the characteristic times of the natural modes of motion of the body divided by wingbeat period are relatively large） compared with many other insects, that the theory based on the averaged model is valid for the hawkmoth means that it could be valid for many insects.     

Computation of field structure and aerodynamic characteristics of delta wings at high angles of attack

A numerical investigation of the structure of the vortical flowfield over delta wings at high angles of attack in longitudinal and with small sideslip angle is presented. Three-dimensional Navier-Stokes numerical simulations were carried out to predict the complex leeward-side flowfield characteristics that are dominated by the effect of the breakdown of the leading-edge vortices. The methods that analyze the flowfield structure quantitatively were given by using flowfield data from the computational results. In the region before the vortex breakdown, the vortex axes are approximated as being straight line. As the angle of attack increases, the vortex axes are closer to the root chord, and farther away from the wing surface. Along the vortex axes, as the adverse pressure gradients occur, the axial velocity decreases, that is, A is negativee, so the vortex is unstable, and it is possible to breakdown. The occurrence of the breakdown results in the instability of lateral motion for a delta wing, and the lateral moment diverges after a small perturbation occurs at high angles of attack. However, after a critical angle of attack is reached the vortices breakdown completely at the wing apex, and the instability resulting from the vortex breakdown disappears.     

Effects of aspect ratio on flapping wing aerodynamics in animal flight

Morphology as well as kinematics is a critical determinant of performance in flapping flight.To understand the effects of the structural traits on aerodynamics of bioflyers,three rectangular wings with aspect ratios（AR）of1,2,and 4 performing hovering-like sinusoidal kinematics at wingtip based Reynolds number of 5 300 are experimentally investigated.Flow structures on sectional cuts along the wing span are compared.Stronger K-H instability is found on the leading edge vortex of wings with higher aspect ratios.Vortex bursting only appears on the outer spanwise locations of high-aspect-ratio wings.The vortex bursting on high-aspect-ratio wings is perhaps one of the reasons why bio-flyers normally have low-aspect-ratio wings.Quantitative analysis exhibits larger dimensionless circulation of the leading edge vortex（LEV）over higher aspect ratio wings except when vortex bursting happens.The average dimensionless circulation of AR1 and AR2 along the span almost equals the dimensionless circulation at the 50%span.The flow structure and the circulation analysis show that the sinusoidal kinematics suppresses breakdown of the LEV compared with simplified flapping kinematics used in similar studies.The Reynolds number effect results on AR4 show that in the current Re range,the overall flow structure is not sensitive to Reynolds number.     

Lift and power requirements of hovering insect flight

Lift and power requirements for hovering flight of eight species of insects are studied by solving the Navier-Stokes equation numerically. The solution provides velocity and pressure fields, from which unsteady aerodynamic forces and moments are obtained. The inertial torque of wing mass are computed analytically. The wing length of the insects ranges from 2 mm (fruit fly) to 52 mm (hawkmoth); Reynolds numbers Re (based on mean flapping speed and mean chord length) ranges from 75 to 3850. The primary findings are shown in the following: (1) Either small (R = 2mm, Re = 75), medium (R ≈ 10 mm, Re ≈ 500) or large (R ≈ 50 mm, Re ≈ 4 000) insects mainly employ the same high-lift mechanism, delayed stall, to produce lift in hovering flight. The midstroke angle of attack needed to produce a mean lift equal to the insect weight is approximately in the range of 25° to 45°, which is approximately in agreement with observation. (2) For the small insect (fruit fly) and for the medium and large insects with relatively small wingbeat frequency (cranefly, ladybird and hawkmoth), the specific power ranges from 18 to 39W·kg^-1 , the major part of the power is due to aerodynamic force, and the elastic storage of negative work does not change the specific power greatly. However for medium and large insects with relatively large wingbeat frequency (hover fly, dronefly, honey bee and bumble bee), the specific power ranges from 39 to 61 W·kg^-1 , the major part of the power is due to wing inertia, and the elastic storage of negative work can decrease the specific power by approximately 33%. (3) For the case of power being mainly contributed by aerodynamic force (fruit fly, cranefly, ladybird and hawkmoth), the specific power is proportional to the product of the wingbeat frequency, the stroke amplitude, the wing length and the drag-to-lift ratio. For the case of power being mainly contributed by wing inertia (hoverfly, dronefly, honey bee and bumble bee), the specific power (without elastic storage) is proportional to the product of the cubic of wingbeat frequency, the square of the stroke amplitude, the square of the wing length and the ratio of wing mass to insect mass.     

Numerical simulation of motion and deformation of ring bubble along body surface

Numerical simulation for fluid flow over an attached rigid body with a deformable ring bubble is analyzed based on the velocity potential theory together with the boundary element method （BEM）. The analysis is focused on the axisymmetric case. The bubble surface is treated as a well defined air-liquid interface and is tracked by a mixed Eulerian-Lagrangian method. The points of intersection between the bubble and body are treated, specially in the numerical procedure. The auxiliary function method is adopted to calculate the pressure on the body surface and in the flow field. The convergence study is undertaken to assess the developed numerical method and the computation code. Some case studies are undertaken in which the interactions between the bubble/body and the incoming flow field are simulated. The effects of various physical parameters on the interactions are investigated.     

A note on the numerical simulations of flow past a wavy square-section cylinder

The flow past a square-section cylinder with a geometric disturbance is investigated by numerical simulations. The extra terms, due to the introduction of mapping transformation simulating the effect of disturbance into the transformed Navier-Stokes equations, are correctly derived, and the incorrect ones in the previous literature are pointed out and analyzed. Furthermore, the relationship between the vorticity, especially on the cylinder surface, and the disturbance is derived and explained theoretically. The computations are performed at two Reynolds numbers of 100 and 180 and three amplitudes of waviness of 0.006, 0.025 and 0.167 with another aim to explore the effects of different Reynolds numbers and disturbance on the vortex dynamics in the wake and forces on the body. Numerical results have shown that, at the mild waviness of 0.025, the Kairmain vortex shedding is suppressed completely for Re = 100, while the forced vortex dislocation is appeared in the near wake at the Reynolds number of 180. The drag reduction is up to 21.6% at Re = 100 and 25.7% at Re = 180 for the high waviness of 0.167 compared with the non-wavy cylinder. The lift and the Strouhal number varied with different Reynolds numbers and the wave steepness are also obtained.     

Non-smooth dynamic modeling and simulation of an unmannedbicycle on a curved pavement

The non-smooth dynamic model of an unmanned bicycle is established to study the contact-separate and stick-slip non-smooth phenomena between wheels and the ground.According to the Carvallo-Whipple configuration,the unmanned bicycle is reduced to four rigid bodies,namely,rear wheel,rear frame,front fork,and front wheel,which are connected by perfect revolute joints.The interaction between each wheel and the ground is simplified as the normal contact force and the friction force at the contact point,and these forces are described by the Hunt-Crossley contact force model and the Lu Gre friction force model,respectively.According to the characteristics of flat and curved pavements,calculation methods for contact forces and their generalized forces are presented.The dynamics of the system is modeled by the Lagrange equations of the first kind,a numerical solution algorithm of the dynamic equations is presented,and the Baumgarte stabilization method is used to restrict the drift of the constraints.The correctness of the dynamic model and the numerical algorithm is verified in comparison with the previous studies.The feasibility of the proposed model is demonstrated by simulations under different motion states.     

Non-smooth dynamic modeling and simulation of an unmannedbicycle on a curved pavement

The non-smooth dynamic model of an unmanned bicycle is established to study the contact-separate and stick-slip non-smooth phenomena between wheels and the ground.According to the Carvallo-Whipple configuration,the unmanned bicycle is reduced to four rigid bodies,namely,rear wheel,rear frame,front fork,and front wheel,which are connected by perfect revolute joints.The interaction between each wheel and the ground is simplified as the normal contact force and the friction force at the contact point,and these forces are described by the Hunt-Crossley contact force model and the Lu Gre friction force model,respectively.According to the characteristics of flat and curved pavements,calculation methods for contact forces and their generalized forces are presented.The dynamics of the system is modeled by the Lagrange equations of the first kind,a numerical solution algorithm of the dynamic equations is presented,and the Baumgarte stabilization method is used to restrict the drift of the constraints.The correctness of the dynamic model and the numerical algorithm is verified in comparison with the previous studies.The feasibility of the proposed model is demonstrated by simulations under different motion states.     

EFFECT OF MAGNETIC NANOPARTICLES ON THE MECHANICAL PROPERTIES OF TYPE-II SUPERCONDUCTORS

In this paper, the effect of magnetic nanoparticles on the mechanical properties of a type-II superconductor is investigated both theoretically and numerically. Magnetic part of the pinning force associated with the interaction between a finite-size spheroidal magnetic inclusion and an Abrikosov vortex is calculated in the London approximation. It is found that the size and shape of magnetic nanoparticles result in different enhancements of vortex pinning in large-κtype-II superconductors. Meanwhile, the screening current induced by a magnetic spheroid suffer the action of Lorentz force, which will lead to prestress in the superconductor, so further numerical calculations are needed to explore the interaction between the spheroidal magnetic particle and superconductor. The distribution of displacement, stress and strain in the superconductor are finally obtained. It is shown that different sizes and shapes of nanoparticles also can change the distributions of these quantities.     

Dynamic analysis on generalized linear elastic body subjected to large scale rigid rotations

The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated. The generalized linear elastic body is described in kine- matics through translational and rotational deformations, and a modified constitutive relation for the rotational deformation is proposed between the couple stress and the curvature tensor. Thus, the balance equations of momentum and moment are used for the motion equations of the body. The floating frame of reference formulation is applied to the elastic body that conducts rotations about a fixed axis. The motion-deformation coupled model is developed in which three types of inertia forces along with their incre- ments are elucidated. The finite element governing equations for the dynamic analysis of the elastic body under large rotations are subsequently formulated with the aid of the constrained variational principle. A penalty parameter is introduced, and the rotational angles at element nodes are treated as independent variables to meet the requirement of C1 continuity. The elastic body is discretized through the isoparametric element with 8 nodes and 48 degrees-of-freedom. As an example with an application of the motion- deformation coupled model, the dynamic analysis on a rotating cantilever with two spatial layouts relative to the rotational axis is numerically implemented. Dynamic frequencies of the rotating cantilever are presented at prescribed constant spin velocities. The maximal rigid rotational velocity is extended for ensuring the applicability of the linear model. A complete set of dynamical response of the rotating cantilever in the case of spin-up maneuver is examined, it is shown that, under the ultimate rigid rotational velocities less than the maximal rigid rotational velocity, the stress strength may exceed the material strength tolerance even though the displacement and rotational angle responses are both convergent. The influence of the cantilever layouts on their responses and the multiple displacement trajectories observed in the floating frame is simultaneously investigated. The motion-deformation coupled model is surely expected to be applicable for a broad range of practical applications.     

Lagrangian-based investigation of the transient flow structures around a pitching hydrofoil

The objective of this paper is to address the transient flow structures around a pitching hydrofoil by combining physical and numerical studies. In order to predict the dynamic behavior of the flow structure effectively, the Lagrangian coherent structures (LCS) defined by the ridges of the finite-time Lyapunov exponent (FTLE) are utilized under the framework of Navier–Stokes flow computations.In the numerical simulations, the k-ω shear stress transport (SST) turbulence model, coupled with a two-equationγ- Reθ transition model, is used for the turbulence closure.Results are presented for a NACA66 hydrofoil undergoing slowly and rapidly pitching motions from 0~?to 15~?then back to 0~?at a moderate Reynolds number Re = 7.5 × 10~5.The results reveal that the transient flow structures can be observed by the LCS method. For the slowly pitching case,it consists of five stages: quasi-steady and laminar, transition from laminar to turbulent, vortex development, large-scale vortex shedding, and reverting to laminar. The observation of LCS and Lagrangian particle tracers elucidates that the trailing edge vortex is nearly attached and stable during the vortex development stage and the interaction between the leading and trailing edge vortex caused by the adverse pressure gradient forces the vortexes to shed downstream during the large-scale vortex shedding stage, which corresponds to obvious fluctuations of the hydrodynamic response. For the rapidly pitching case, the inflection is hardly to be observedand the stall is delayed. The vortex formation, interaction, and shedding occurred once instead of being repeated three times,which is responsible for just one fluctuation in the hydrodynamic characteristics. The numerical results also show that the FTLE field has the potential to identify the transient flows,and the LCS can represent the divergence extent of infinite neighboring particles and capture the interface of the vortex region.     

Influences of aerodynamic loads on hunting stability of high-speed railway vehicles and parameter studies

The influences of steady aerodynamic loads on hunting stability of high-speed railway vehicles were investigated in this study.A mechanism is suggested to explain the change of hunting behavior due to actions of aerodynamic loads：the aerodynamic loads can change the position of vehicle system（consequently the contact relations）,the wheel/rail normal contact forces,the gravitational restoring forces/moments and the creep forces/moments.A mathematical model for hunting stability incorporating such influences was developed.A computer program capable of incorporating the effects of aerodynamic loads based on the model was written,and the critical speeds were calculated using this program.The dependences of linear and nonlinear critical speeds on suspension parameters considering aerodynamic loads were analyzed by using the orthogonal test method,the results were also compared with the situations without aerodynamic loads.It is shown that the most dominant factors a ff ecting linear and nonlinear critical speeds are different whether the aerodynamic loads considered or not.The damping of yaw damper is the most dominant influencing factor for linear critical speeds,while the damping of lateral damper is most dominant for nonlinear ones.When the influences of aerodynamic loads are considered,the linear critical speeds decrease with the rise of cross wind velocity,whereas it is not the case for the nonlinear critical speeds.The variation trends of critical speeds with suspension parameters can be significantly changed by aerodynamic loads.Combined actions of aerodynamic loads and suspension parameters also a ff ect the critical speeds.The effects of such joint action are more obvious for nonlinear critical speeds.     

Nonstationary plane contact problem in theory of elasticity for conformal cylindrical surfaces

A numerical–analytical approach is described to investigate the process of impact interaction between a long smooth rigid body and the surface of a circular cylindrical cavity in elastic space. A non-stationary mixed initial boundary value problem is formulated with a priori unknown boundaries moving with variable velocity. The problem is solved using the methods of the theory of integral transforms, expansion of desired variables into a Fourier series, and the quadrature method to reduce the problem to solving a system of linear algebraic equations at each time step. Some concrete numerical computations are presented.The cylindrical body mass and radius impact on the proile of the transient process of contact interaction has been analysed.